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Topic: Matheology � 300
Replies: 27   Last Post: Jul 9, 2013 2:50 PM

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LudovicoVan

Posts: 3,201
From: London
Registered: 2/8/08
Re: Matheology § 300
Posted: Jul 7, 2013 4:32 PM
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"Michael Klemm" <m_f_klemm@t-online.de> wrote in message
news:krchad$adn$1@solani.org...
> Julio Di Egidio wrote:
>

>> Again, that for all n in N the value is 1/oo just does not entail that
>> the limit is 1/oo.

>
> If you accept that 1/oo is a natural not
> depending on the natural n, then the limit n->oo of
> the constant sequence (1/oo, 1/oo, ...) is 1/oo.
> The way how the number 1/oo is obtained
> doesn't matter.


Well, I do not see how that can be acceptable. The original expression has
a sub-expression dependent on n under the limit, not just a constant value.
Again, that the sequence is constant for all n in N does not entail that the
limit for n->oo must be equal to that constant value.

Indeed, by your token:

lim_{n->oo} Card(N\F(n)) = oo (1)

yet:

lim_{n->oo} N\F(n) = {} (2)

or is that supposed to be N, too??

At least, I suppose we'd agree that:

lim_{n->oo} F(n) = N (3)

Of course, I am assuming that the limit of the cardinality of our
well-founded sequence is equal to the cardinality of the limit of the
sequence. I still do not see how we could define the limit otherwise (I may
be missing formal details), but even less I can see (1) compatible with (2).

Julio





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